They way I understand "General Bloodmanes" (non-phenotypic) is that sibkos are still produced with a specific goal in mind by the scientists and Bloodname House leaders who arrange these things. A General name (such as Kerensky, Fetladral, Hazen, McKenna, Crow, Kotare, etc...) could have MechWarrior sibkos, Aerospace Fighter sibkos or even Elemental sibkos (with the additions of the corresponding Bloodline of that type). So general names can produce "General" types of human beings, or they could be used to seed a phenotype sibko IF their genes were combined with those of a phenotype.
Would this be correct?
(I'm trembling in fear and awe of the thought of angry Hazen Elementals armed with vibro-katanas, or worse, Khatib Elementals waiting to thump people on the skull with their Holy Books...)
(I also realize different Clans have different practices. The Jade Falcon sibkos seem to be specific, while the Wolf sibkos are mixed up, both in phenotypes and bloodlines, thus Vlad, Rana, Carew and Evantha all saying to each other "do it for the sibko!")